How to save an image in uv editor even when closing blender?
Setup your image(s) however you would like before modifying anything else in a new clean .blend file.
Press Ctrl+U to save the modified start-up file as the new default, and the images (along with any other changes, materials, objects, etc.) will be present going forward.
If you decide to go back to the default configuration, then you can Load Factory Settings
Documentation is here